“Galileo got it wrong. The Earth does not revolve around the Sun. It revolves around you and has been doing so for decades. At least, this is the model you are using.” -Srikumar Rao

It’s the end of the week, so that means its time to take on another one of your questions from the question/suggestion box, and continue our ongoing Ask Ethan series! Even though there’s a backlog of hundreds of questions, you should keep sending the new ones in, as all questions are fair game for any segment. This week’s question comes from reader Brian Mucha, who asks us:

Where did the sun and planets get their angular momentum resulting in their rotation. I am not asking about the orbits but the actual rotation. I understand the ice skater analogy where bringing in the extended arms increase the skaters rotation due to the conservation of angular momentum. But the skater starts with spin. IF the skater is standing still they can extend and retract their arms all day and they wont spin.

So when the planets and the sun started to form how was their initial angular momentum achieved?

Ahh, the old question of rotation, and why everything does it.

Image credit: Alicia of http://surrenderingallofme.blogspot.com/.

It’s easy to make something spin faster once it’s already going: you just change its moment of inertia.

What does that term mean, moment of inertia?

Image credit: PDFcast and Utah Electronic High School

You know Newton’s second law: the one that tells you force is equal to mass times acceleration (F = ma). Technically, it’s a little more accurate to say that force is how another quantity — momentum — changes over time. It means if you apply any external force to a mass, its momentum — or how it’s currently moving — will change, and it tells you exactly by what amount it will change. And if you don’t apply an external force to something, its momentum cannot change.

And if everything in the entire Universe only consisted of point masses along the same line, we’d never need anything else. But in the real Universe, masses-in-motion are distributed in more than one dimension.

Image credit: Greg L at the English language Wikipedia.

And whenever you have that, your system has not just momentum, but also angular momentum. And while momentum changes are dependent on mass, angular momentum changes are dependent on a combination of the mass and how that mass is distributed. That combination of factors — mass and how it’s distributed — is what makes up moment of inertia. So yes, Newton’s second law relates how objects change their momentum (i.e., how masses experience changes in their velocities), and there’s an equivalent law that relates how objects change their angular momentum, or how moments of inertia experience changes in their rate of rotation.

Images credit: Markus Pössel, Einstein Online Vol. 3 (2007), 1011.

How the figure skater who pulls her arms and legs in spins faster is one example of this: as her mass becomes distributed closer to the axis-of-rotation (and her moment of inertia gets smaller), her rotation rate increases to compensate. If your mass-and-how-it’s-distributed changes (goes up or down), your rate of rotation will also change (go down or up) to compensate. But just like Newton’s second law tells you that you can change a system’s momentum by applying an outside force, you can change a system’s angular momentum by applying an outside torque.

Image credit: Wikimedia Commons user Yawe.

And a torque is just a force applied in such a way that it causes an object’s rotation to change.

Image credit: NASA, ESA, and the Hubble Heritage Team (STScI/AURA).

Now here’s where it gets interesting: every star system in the Universe once began as a cloud of gas-and-dust. These clouds may have been thousands or millions (or in some rare cases, maybe even larger) of times the mass of our Sun, but they were once incredibly diffuse, and spread out across many hundreds or thousands of light years. If these gas clouds had (or the ones we see today have) any sort of global rotation to them, it’s far too small to be detectable, as it would take billions of years for such a gas cloud to make even one complete rotation.

Image credit: NASA/ESA and The Hubble Heritage Team (STScI/AURA)

But gas clouds — like all objects in the Universe — don’t exist in isolation. They exist in the presence of all the other matter-and-energy in the Universe, all of which is subject to the laws of gravitation. And whenever any two masses in the Universe are in relative motion to one another, so long as they’re not moving exactly and directly towards-or-away-from one another, the gravitational force they exert on each other causes a torque.

Illustration credit: Bill Saxton, NRAO / AUI / NSF.

This phenomenon is known as a tidal torque, and was first theoretically understood by Jim Peebles — my Ph.D. advisor’s Ph.D. advisor (or my grand-advisor) — back in 1976. (So, you asked the right person!) It’s why pretty much every mass that exists in this Universe, whether it was born with non-zero angular momentum or not, has one now, 13.8 billion years onward. That includes every gas cloud, including the one that gave rise to our Solar System. We can break these large gas clouds up further, into the regions that give rise to the individual stars and star systems that came into existence.

Each one of these regions that eventually result in a star/star system, with whatever angular momentum they have inside, are typically distributed in shapes known as triaxial ellipsoids. A triaxial ellipsoid is a fancy way to say that they’re like spheres, except inevitably if you draw three perpendicular axes on them (X, Y, and Z, for example), one of the axes will inevitably be the shortest of the three. When a region gravitationally collapses, it’s going to collapse along the shortest axis the fastest, and because normal matter — the stuff all stars and planets is made out of — interacts (i.e., collides) with itself, that means it’s going to go “splat,” like a pancake. (In fact, the scientific word for this process is known as pancaking.)

Image credit: NASA / JPL-Caltech.

But along the other two axes, you’ll have a disk-like distribution, which is going to have an overall, net rotation in the direction of whatever its angular momentum is! It’s the reason why — in our Solar System — all the planets revolve around the Sun in the same direction (counterclockwise, looking downwards from north of the Sun’s north pole), the Sun rotates in that same direction, almost all the moons revolve around their planet in that same direction (with notable exceptions explained here), and finally, why practically all the planets rotate about their axes in that same direction, too.

Image credit: Calvin Hamilton, and click for a huge version!

There are only two major exceptions to the rule: Venus, which hardly rotates at all (but does so in the opposite direction), and Uranus, which rotates practically on its side. Both of these worlds are thought to have had their angular momentum significantly changed by the intervention of an outside body, most likely a significant collision a long time ago. That is to say, their rotation was changed by the influence of an external torque!

Image credit: Bhavana Jagat, via http://bhavanajagat.com/.

So that’s the story of why planets, moons, stars and star systems revolve and rotate the way they do! Thanks for a good question, Brian, and to anyone else who has a question or suggestion for me, drop me a line!

Comments

Could be my fault… but I’m not convinced by what I’ve read here Ethan.

I’m still rather amazed that a solar system resolves into a 2D disk from [I assume] a random set of particles in 3D. I think I would be happier if I had some idea the range of torques that could fall out of a *typical* solar system

I would assume that a typical pre-solar system should have zero spin on average, but obviously I’m wrong

The initial spin is just gravity. If you have an amorphous blob of stuff, pick any point in the stuff, and every other bit of mass in the stuff is going to exert gravity on it. Now repeat that for every point within the blob of stuff. These forces are not going to be equal, hence it will accelerate (rotate). Unless the initial form were a perfectly uniform sphere, (I think) this will happen.

I’m guessing that it would eventually just begin rotating about the centroid of the inital blob of stuff.

As gravity continues to form more cohesive masses out of the stuff, this is where change in mass distribution and conservation of angular momentum kicks in and compels it to form a disc, (and spin faster?). (spin a water filled balloon about an axis and it would have the same effect).

I think I have that more or less right, though I’m just going off of a year of University physics, and several years of reading Ethan’s blog here… so … yeah.

The Oort cloud rotates in many difference axises, and that is unstable since they cross each others path a lot, causing all these comets to bomb into us.

But that far out, they’re very diffuse so interactions are not common.

Closer in, those off-ecliptic orbits were destroyed by much more frequent interactions and they bombarded the inner solar system. See the Moon’s backside.

Once crashed, they aren’t orbiting any more, so they don’t exist much.

(note: only one method for the weeding out. There’s still a preferential axis that everything would have “just picked” because perfect isometry is impossible and the biggest mass there (the sun) would be displaying a rotation around that axis more than any other.)

For a start, that part of the dust matter closer to the centre of mass of the galaxy would lose velocity when “pulled” back out by in-falling to the new sun, and that further out would gain velocity when “pulled” back in.

But even absent that, zero has a 0/1 chance (infinitesimally small) of occurring.

@Michael Fisher #1: I thought Ethan explained it relatively clearly, but he did skip some steps in the argument (citing external papers instead).

Addressing your questions in reverse order.

1) Why did the presolar nebula have non-zero angular momentum initially? The answer to that is _tidal_torque_. Consider the simple case of two separated blobs of extended matter (gas clouds, dust clouns, galaxies, whatever). Suppose these are the only things in the Universe. What happens? Tides! Since the blobs are extended, there will be different gravitational forces on the near vs. far sides, and also on the “left vs. right” sides (unless both blobs just happen to be perfectly spherical). If the blobs are moving relative to one another, then there will in general be a non-zero impact parameter between their centers (that is, they will zip past one another, not collide head on). Put those things together, and you should be able to work out that the two blobs extert a net torque on one another, with the result that each one — even if initially irrotational! — will start rotating.

2) Why does a non-spherical 3D matter distribution evolve into a 2D disk? “Pancaking.” Start with a distribution, which can be perfectly spherical or not, with net angular momentum about some axis Z (see item (1) above). Gravity alone would pull that 3D distribution inward radially, making a smaller and smaller blob, until pressure or solidity or whatever made it a little sphere (this is the “hydrostatic equilibrum” referred to in the IAU definition of a planet!). But we just said the blob is spinning. For the part of gravity pulling bits together along Z, the angular momentum doesn’t change. But for the part of gravity pulling perpendicular to Z, moving bits closer to the axis means either (a) angular momentum must disappear; or (b) tangential speed must increase to conserve angular momentum. But increasing the tangential speed of a bit about the center pushes that bit to a _larger_ orbit, even though gravity is trying to pull it to a _smaller_ one! The net result? In the plane perpendicular to Z, stuff stays roughly where it started, but along Z, stuff collapses down. So you go from a 3D blob to a 2D-ish pancake (2D up to a thickness corresponding to pressure-balance).

Michael #6 and all: I think pancaking can be shown very effectively by putting a small ball of water to rotation somewhere within the ISS. We’ve seen several watery experiments on the ISS, but I don’t recall pancaking being one of them. I think that would be a cool experiment to see…

I think I see why solar systems spin the way they do. Because gas and dust clouds that don’t will never condense into solar systems. The material that starts to form a disk has to rotate or it falls out of the sky and, in the process, builds up the central mass that will evolve into a sun. If enough matter does, rotation of the amorphous blob develops into revolution (in the same direction) of discrete objects. The ones that survive as planets or asteroids are the ones that are moving at the right speed and distance to balance gravitational forces.
But it’s the persistence of the link between rotation and revolution that puzzles me.
I’m not quite clear what causes planets to rotate in the same direction as they revolve. I can see the sun tugging against counter-rotation, much as Earth has pulled the moon’s rotation to a standstill, but planets generally spin faster than they revolve. And I wonder if Venus and Uranus will ever have to pay a price for their waywardness.
If we zoom out, our solar system behaves toward the galaxy much like such a rogue planet – revolving the same way the Milky Way rotates, but at a wicked angle. Is this a big mistake on our part? Could that play a role in our predicted fate of crashing into Andromeda? Not that there’s much we could do to change things at this point. Let’s just try to enjoy the ride, I guess.

@Tihomir #7: I don’t think you can use water blobs in microgravity to show pancaking. The problem, as I see it, is that they don’t have an attractive potential (i.e., something trying to pull them toward their center).

They have a surface tension, which is going to pull tangentially everywhere, which gives you a “vertical” pull along the rotation axis down at the equator, but a “radial” pull _toward_ the rotation axis up at the poles.

What you might get with a well-formed but spinning water blob is a sphere with an equatorial rim.

Your explanation and the comments that followed, all explain why the universe evolved into what we see today and I understand this, but it does not explain why the gas left over after inflation, just after the big bang would have any angular momentum at all. Without that initial angular momentum, the gas should have simply collapsed back into a singularity. Obviously, it did not, so some initial angular momentum was present, no matter how small. Also the distribution of mass within the cloud of gas was not uniform. I have read that the non-uniformity of mass can be explained by quantum fluctuations, but no explanation of the initial angular momentum has ever, to my knowledge, been suggested. Quantum fluctuations do not seem to work as an explanation either.
I think that this was the actual question posed here. Not how did the objects in the universe end up spinning the way they did, but where the initial momentum came from that allowed that spin to evolve.

Okay Folks, why would some thing begin to exert gravitational force when its a particle, under what unknow circumstances whould these particles move or change direction when everything to begin was in rest, and please how in this world can you come up with past billions of years of story when real time any idea or theory is just few years old…ITS LIKE AND ANT ON ROAD TRYING TO WRITE A THEORY ON A CITY WHEN HE HAS NO MEANS OF PHYSICALLY /MENTALLY KNOWING WHAT N WHERE TO LOOK …
If you still trust Newton laws….then at all times things are in Equilibrium. why would a change to begin with …Why should gravity of A should intervene the gravity of B in space.

@Paul #10: This is the same question Michael Fisher asked, and which both Ethan and I have tried to answer. Non-spherical blobs of matter exert and respond to gravity with both “central forces” (the usual F = -GMm/r^2) _and_ with torques. In this case, the torque arises because there are different forces acting on different parts of the non-spherical blob.

If the blob is holding itself together (either graviationally or with chemical/EM forces), then those differential forces will _cause_ a rotation of the object, even if it wasn’t rotating before.

Thinktank, if you’re going to berate everyone for being dumber than you, you’d best stop for a bit, calm down and collect your thoughts.

Because SOMETHING is making your post full of bad English.

Then work on what it is you’re trying to say. Because I’m sitting here thinking “Well what the hell do you mean there?” and having to interpret it to something that is coherent.

With that out of the way:

“why would some thing begin to exert gravitational force when its a particle”

Because it has gravitational mass and therefore transfers energy by the force of gravity to things within range.

“under what unknow circumstances whould these particles move or change direction when everything to begin was in rest”

Who says it was at rest? This isn’t an explosion where the bomb was sitting still, someone lit the fuse and it went BOOM.

“and please how in this world can you come up with past billions of years of story when real time any idea or theory is just few years old”

By looking at the physics of distant stars and determine that the physics hasn’t changed appreciably in that time. E.g. the value of the fine structure constant is a combination of several fundamental constants and if they change, the laws of physics change.

There’s no change.

“ITS LIKE AND ANT ON ROAD TRYING TO WRITE A THEORY ON A CITY WHEN HE HAS NO MEANS OF PHYSICALLY /MENTALLY KNOWING WHAT N WHERE TO LOOK”

No it isn’t.

“If you still trust Newton laws….then at all times things are in Equilibrium”

Paul, what Michael is saying is that for a collapse not to AUTOMATICALLY result in increased rotation would require the gravitational field over the entire size of the collapsing cloud to be flat. Absolutely flat.

Otherwise by pulling it out of its current location it would experience a force that will cause it to deviate from the straight line to the CoM because it’s in a different gravitational potential field.

This is my favorite version of Wow. I like this one better than the mean one. Argument destroyer, not self-esteem destroyer, although the latter does have it place in the very rare exception. Just my opinion though.

the universe was never static. Even at earliest stages. There was some intrinsic motion (however small) emparted to matter from leftovers of inflation. Then as you said youself, the small non-uniformities caused local attractions (gravity)

I’m not quite clear what causes planets to rotate in the same direction as they revolve.

I haven’t seen anybody else answer Chuck’s question @8, so I’ll give it a try.

Gravity is trying to pull mass toward the center of the disk, but in order to move inward any given bit of mass would have to lose orbital angular momentum. So if a bunch of that mass starts spinning in the same direction as the orbital motion, that spin angular momentum can absorb some of the orbital angular momentum and allow that bit of mass to fall inward. To get some mass to rotate in the opposite direction, you would have to increase its orbital angular momentum to compensate, and gravity opposes that. So while it’s not impossible to get retrograde rotation, it requires external torques, as Ethan points out in the original post.

Regarding spin rates vs. orbital rates, keep in mind that that is only one of the two factors which go into angular momentum, the other being the mass distribution. Planets orbit a star at a distance much larger than their radii, so despite the much lower angular velocity the orbital angular momentum can be comparable to, or even larger than, the spin angular momentum.

it does not explain why the gas left over after inflation, just after the big bang would have any angular momentum at all.

It doesn’t have to. It does, for reasons people have already given, but we can start with a universe without any and get galaxies, solar systems, and planets that rotate.

A layman version goes like this: the interactions between particles or masses converts gravitational energy into momentum. Start with two sationary balls apart, and gravity, and they will start slowly moving together. Right? That’s very intuitive. The exact same statement is true – but less intutive – for torque. Start with two objects without any torque, plus gravity, and (with a couple of wierd exceptions), they will acquire torque.

The wierd excetions are point masses and perfectly spherical masses. But otherwise, your two objects are not only going to start moving towards each other, but different parts of each object are going to gain microscopicaly different momenta. That results in a tumbling motion and leads to rotation.

@Rich T #21: That’s a bit of an unanswerable question, kind of like asking, “What is the velocity of the universe considered as a single entity?” In order to measure a net rotation of the whole observable universe, you would need to be able to observe it with respect to some external reference frame. “External” and “whole observable universe” are mutually exclusive.

Rich T:
If the universe were rotating, that would be in relation to what? The picture is that there is no space “beyond” the universe, nor is there a time according to which a dynamic process like rotation could be said to occur. So there’s nothing to rotate in.

If there’s a multiverse and some intervening space between our universe and another, then we might be able to talk about rotation. But that doesn’t seem like a promising scenario, because if it’s the same space as our three dimensions, I don’t see how we’re talking about a “universe” instead of “part of a universe.” And if it were rotation in some other dimension, it seems that whatever it is must not be ordinary angular momentum at all.

Could one still measure net angular momentum of the universe if it was rotating strongly in one direction? My understanding is that the Cosmological Principle would state that the universe is isotropic, and a universe with a preference for a certain spin wouldn’t be isotropic, I feel like that’d be a significant symmetry break.

It’s my understanding that the while random solar systems or galaxies might have a net angular momentum, there is no reason why galaxies couldn’t spin opposite directions, so the overall universe would have zero, or nearly zero net angular momentum.

I could, of course, be very wrong, as I’m but a BsC. PS, I had a prof from SLAC, she was awesome, seems like that’s a great place to work.

So why doesn’t pancaking happen to planets and the sun just like the whole (solar) system? I know they do flatten a little at the poles. Do the multiple moons around some planets rotate in one plane from pancaking, and if not, why not?

So why doesn’t pancaking happen to planets and the sun just like the whole (solar) system? I know they do flatten a little at the poles.

In planets and stars, the atoms are also interacting via the electromagnetic force, strong force, and weak force. These counteract gravitational pancaking. So, for example, the Earth can’t pancake because the atoms on the surface are being electromagnetically pushed “up” (away from center) by the atoms underneath them. For stars and in particular neutron stars, the strong force does the same job.

Do the multiple moons around some planets rotate in one plane from pancaking, and if not, why not?

I believe the answer to this question is: the pancaking was a solar-system-wide effect that imparted approximately the same directional momentum to pretty much all the atoms in it. That’s why pretty much everything in our solar system rotates more or less in the same plane and direction. The exceptions (moons orbiting in the wrong direction, etc…) are a result of collisions or non-local objects being captured by a local system, or both.

Thinking over the shape of the equations, eric, I rather think that frame dragging would retard the effect. Except that frame dragging would tend to be where there’s already a lot of rotation going on, so it’d still be “Gotta pancake” overall.

And the volume which even a super massive massive black hole would have its effect even in the dense core would have it include very few actual stellar bodies.

“in Euclidean geometry.. three categories of objects, points, lines, and planes.. are not defined but assumed to be intuitively given.” Herman Weyl, pg 3, Philosophy of Mathematics and Natural Science, 1949

then Weyl, pg 105, “Incidentally, without a world structure, the concept of relative motion of several bodies has, as the postulate of general relativity shows, no more foundation than the concept of absolute motion of a single body.”

Then we have, “After the Godel discovery of rotating model universe, several other rotating cosmological models were discovered with interesting properties different from the Godel model universe.” pg 243, Gravitation and Inertia, Ignazio Ciufolini and John Archibald Wheeler, 1995

So it seems we have a kind of a chicken and an egg situation regarding the possibility of a observing our visible universe as a rotating universe. we need clear concept is our visible universe rotating relative to space or time or relative to extra dimensions or relative to its own space time or what? I defer to the experts on what a more correct testable question might be?

But then Ciufolini and Wheeler suggest, “for example, one can put limits to the rotation of the universe using upper limits to the large scale anisotropy of the cosmic blackbody radiation.. Test of non rotation of the universe.. for example, using, VLBI and local gyroscopes” pg 251 Just which definition of rotation are they using? I don’t know but I assume a closed GR universe.

So the question of what it might mean to even ask and then to answer, is our visible universe rotating (and relative to what)?; seems a valid scientific question.

And the best answer to date seems to be http://www.earlyuniverse.org/is-the-universe-rotating/ ” we have studied models of rotating universes, the so-called Bianchi models, in order to test the isotropy of the Universe… So, is the Universe rotating? Well, probably not… However, only very simple Bianchi models have been compared to the data so far. There are more sophisticated Bianchi models that more accurately describe the physics involved and could perhaps even provide a better explanation of CMB observations. We’re looking into it!”

So it’s a difficult question. Very difficult mathematics (because “only very simple Bianchi models have been compared”) and very difficult physics (because a century of observation needs to be explained in the detail).

But there are, “two types of scientific development, normal and revolutionary.. normal science is what produces the bricks that scientific research is forever adding to the growing stockpile of scientific knowledge… Revolutionary changes are problematic. they involve discoveries that cannot be accommodated within the concepts in use before they were made.” Thomas Kuhn, the road Since Structure, pg 14

In my opinion the question of whether the universe is rotating or not (and what that means) is tied up with other questions such as what is dark matter and energy, are there extra-dimensions, is there only one dimension of time, etc.

If we are to consider “revolutionary scientific development” and not just “normal scientific development”; then we need to be open to understanding (even in very fuzzy terms) what the range of possible universes are, i.e. some very crazy speculative ideas.

That is, if we consider that “revolutionary cosmology” development is still possible and not just “normal stockpiling of more cosmological bricks” from here on out.

Yep, yuk, yuk, just dumb luck we got it all basically right in the 20th century.

This mathematically sophisticated physicist suggests http://arxiv.org/pdf/1303.3044v2.pdf Stable Cosmic Vortons “We present for the ﬁrst time solutions in the gauged U(1) U(1) model of Witten describing vortons – spinning ﬂux loops stabilized against contraction by the centrifugal force… We construct explicitly a family of stationary vortons characterized by their charge and angular momentum. Most of them are unstable and break in pieces when perturbed… until recently it was not clear whether cosmic vortons were stable or not… Interestingly, a very similar conclusion was made for the ‘spinning light bullets’ which share many ideas with vortons.” (Nice try, seriously crazy enough. And even almost ready to be explained in everyday English. Maybe with vortons we get a rotating universe. Probably not that easy. Do we have to go back to the Bianchi models?)

Well anyway or NOT, I personally expect to see “revolutionary cosmology” in my lifetime not just “”normal stockpiling of more cosmological bricks.”

Well anyway or NOT, I personally expect to see “revolutionary cosmology” in my lifetime not just “”normal stockpiling of more cosmological bricks.”

Good lord, man! In the last human lifetime we’ve gone from the steady state model to simple big bang to inflationary big bang. We’ve gone from thinking we understand just about everything in the universe to thinking we understand about 5% of its mass and energy.

This IS a revolutionary period in cosmology. You’re living in one right now. Cosmological sciences 1930-2030 is what a scientific revolution looks like.